Our first approach is based on sparsification via the notion of effective resistances [1]}, which
depends on the concentration properties of the sums of random outer-products and was originally developed for sparsification of weighted graph Laplacians. Similar to graph Laplacian, the frame matrix \({\bf S}\)  is also a sum of rank-one matrices
\({\bf S}=\sum _{\phi \in \Phi } \hspace{1.42271pt}\phi \phi ^T.\) 
